If α+β=90α+β=90, simplify cosαcosecβcosαsinβ.cosαcosecβcosαsinβ.


Answer:

±sinα±sinα

Step by Step Explanation:
  1. It is given that α+β=90α+β=90
    β=90αβ=90α
  2. Replace ββ with 90α90α in given expression.
    cosαcosecβcosαsinβ=cosαcosec(90α)cosαsin(90α)=cosαsecαcosαcosα=1cos2α=±sinα

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